How Ordinary Elimination Became Gaussian Elimination
For historians of mathematics, this paper clarifies the misattribution of Gaussian elimination to Gauss, revealing the role of professional computers in popularizing the method.
The paper traces the historical development of Gaussian elimination, showing how a method initially described by Newton and later applied to linear equations by various mathematicians became named after Gauss due to specialized notation he devised for least squares calculations.
Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre called "ordinary," and that Gauss called "common" - is now named after Gauss: "Gaussian" elimination. Gauss's name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices.